Question

Which of the following statements are true?
a. If an object's speed is constant, then its acceleration must be zero.
b. If an object's acceleration is zero, then its speed must be constant.
c. If an object's velocity is constant, then its speed must be constant.
d. If an object's acceleration is zero, its velocity must be constant.
e. If an object's speed is constant, then its velocity must be constant.

Answer 1

Answer:

a. If an object's speed is constant, then its acceleration must be zero.

FALSE

As we know that acceleration is defined as the rate of change in velocity

$a = \frac{d\vec v}{dt}$

so we can not say anything about the acceleration when speed is given to as and no information is given about velocity

b. If an object's acceleration is zero, then its speed must be constant.

TRUE

As we know that acceleration is defined as the rate of change in velocity

$a = \frac{d\vec v}{dt}$

Since we know that if acceleration is 0 then velocity must be constant and hence speed is also constant

c. If an object's velocity is constant, then its speed must be constant.

TRUE

Since velocity is constant then it shows that its magnitude and direction both are constant so its speed is also constant.

d. If an object's acceleration is zero, its velocity must be constant.

TRUE

As we know that acceleration is defined as the rate of change in velocity

$a = \frac{d\vec v}{dt}$

Since we know that if acceleration is 0 then velocity must be constant

e. If an object's speed is constant, then its velocity must be constant.

FALSE

Speed is just the magnitude so we can not say about its direction and hence if speed is constant then velocity may or may not change